| Project/Area Number |
02452010
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyushu University |
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Principal Investigator |
TANAKA Syunichi Kyushu Univ., Faculty of Sci., Professor, 理学部, 教授 (00028127)
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| Co-Investigator(Kenkyū-buntansha) |
OHTSUKA Hiroshi Kyushu Univ., Faculty of Sci., Assistant, 理学部, 助手 (30203839)
KAWASAKI Hidefumi Kyushu Univ., Faculty of Sci., Lecturer, 理学部, 講師 (90161306)
NAKAO Mitsuhiro Kyushu Univ., Faculty of Sci., Associate Professor, 理学部, 助教授 (10136418)
YANAGAWA Takashi Kyushu Univ., Faculty of Sci., Associate Professor, 理学部, 助教授 (80029488)
FURUKAWA Nagata Kyushu Univ., Faculty of Sci., Professor, 理学部, 教授 (50037165)
山本 野人 九州大学, 理学部, 助手 (30210545)
河原 康雄 九州大学, 理学部, 助教授 (90091181)
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| Project Period (FY) |
1990 – 1991
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| Project Status |
Completed (Fiscal Year 1991)
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| Budget Amount *help |
¥6,400,000 (Direct Cost: ¥6,400,000)
Fiscal Year 1991: ¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1990: ¥3,800,000 (Direct Cost: ¥3,800,000)
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| Keywords | Complex Systems / Formal Methods / Axiomatic Set Theory / Concurrency / Nonstandard Analysis / 並行プロセス / 述語論理 |
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| Research Abstract |
The purpose of this project is to study possible relations between computing science and complex systems such as brain and market. As yet no secure theoretical foundation for studying these systems is available, we tried to search the one. The candidate is Formal Mathematics and Science based on the axiomatic set theory. Nonstandard Analysis is an important example in mathematics. In information and languages, Milner's Process Calculus and Barwise's Situation Theory (for natural languages) are formalized on non-well-founded set theory (developed by Aczel). These independent developments suggest the unity of various formal methods.
Neural network theory is a dynamical aspects of a complex system. Infinitesimals and hyperfinite integers of nonstandard analysis may give us new perspective on large finite dynamical systems.
Details of above observations are contained in the accompanying report.
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